Information geometric similarity measurement for near-random stochastic processes

Abstract

We outline the information-theoretic differential geometry of gamma distributions, which contain exponential distributions as a special case, and log-gamma distributions. Our arguments support the opinion that these distributions have a natural role in representing departures from randomness, uniformity, and Gaussian behavior in stochastic processes. We show also how the information geometry provides a surprisingly tractable Riemannian manifold and product spaces thereof, on which may be represented the evolution of a stochastic process, or the comparison of different processes, by means of well-founded maximum likelihood parameter estimation. Our model incorporates possible correlations among parameters. We discuss applications and provide some illustrations from a recent study of amino acid self-clustering in protein sequences; we provide also some results from simulations for multisymbol sequences.